One of the most interesting features
of the QHO is the construction of its coherent states as the
eigenfunctions of the annihilation operator. As is well known
[1]}, one can introduce nonlinear coherent states (NLCSs)
or \(f\) -coherent states as the right-hand eigenstates of the deformed
annihilation operator \(\hat{A}\) . It has been shown [2]}
that these families of generalized coherent states exhibit various
non-classical properties. Due to these properties and their
applications, generation of these states is a very important issue
in the context of quantum optics. The \(f\) -coherent states may appear
as stationary states of the center-of-mass motion of a trapped ion
[3]}. Furthermore, a theoretical scheme for generation of
these states in a coherently pumped micromaser within the
frame-work of intensity-dependent Jaynes-Cummings model has been
proposed [4]}.
